Distance between a line and a point calculator

This online calculator uses the line-point distance formula to determine the distance between a point and a line in the 2D plane.

Find the distance from line $L : y = x$ to the point $(0, 0)$ .

solution

The distance between the line and the point is:

d = 0

explanation

The distance from the point $(x_{0}, y_{0})$ to the line $A x + B y + C = 0$ is given by:

d = \frac{∣ A x _{0} + B _{y} o + C ∣}{A ^{2} + B ^{2}}

To apply this formula, we first need to express the line in standard form

y x - y = x = 0

After substituting: $A = 1$ , $B = - 1$ , $C = 0$ , $x_{0} = 0$ and $y_{0} = 0$ we have:

d = d = d = d = d = \frac{∣ 1 \cdot 0 + ( - 1 ) \cdot 0 + 0 ∣}{1 ^{2} + ( - 1 ) ^{2}} = \frac{∣ 0 + 0 + 0 ∣}{1 + 1} = \frac{∣ 0 ∣}{2} = \frac{0}{2} = 0

Download Png

Distance between a line and a point

supports lines in both standard and slope-intercept form
help ↓↓ examples ↓↓

0123456789–/.√C ✖

Input line in:

Line equation:

= 0

y = x

Input point:

( , )

Settings:

Hide graph

Hide steps

Find approximate solution

thumb_up 2.1K thumb_down

working...

Hire MATHPORTAL experts to do math homework for you.

Prices start at $3 per problem.

Examples

ex 1:

Find the distance from the line 3x+4y-5= 0 to the point point (-2, 5).

ex 2:

Find the perpendicular distance from the point (5, -1) to the line y = 1/2x + 2

ex 3:

Find the perpendicular distance from the point (-3, 1) to the line y = 2x + 4.

Related calculators

Find more worked-out examples in our database of solved problems.

Search our database with more than 300 calculators

452 861 664 solved problems